It was not in the interest of AIG, its shareholders or the public to sue the U.S. over the terms of its bailout but Hank Greenberg will continue with his lawsuit, CEO Robert Benmosche told CNBC's "Closing Bell" on Wednesday.

"It's not acceptable socially for AIG to have taken this money and think that we could come back and sue the government because you [the government] made too much money on the deal," he said. "It may be a bad deal, but a deal's a deal."

Last summer the courts asked AIG to decide whether it wanted to join former AIG Chief Executive Hank Greenberg in his lawsuit alleging the rescue was unfair to shareholders and that the Federal Reserve Bank of New York charged an excessive interest rate on its initial loan. He has sought billions of dollars in damages.

Greenberg's Starr International owned 12 percent of the insurer at the time of its rescue.

"It's not in the interest of AIG, our policyholders, our clients or employees as well as our shareholders and the public at large, it wasn't in AIG's interest to proceed or have Greenberg proceed on AIG's behalf," Benmosche said.

Greenberg is still free to proceed with his lawsuit on behalf of shareholders.

Benmosche said that AIG is now looking forward. "My view right now is we had to pay back America. It came with a profit. We have strong, vibrant company. We're thanking America and we have to go forward," he said.

AIG's property/casualty, the mortgage insurance, and life and retirement businesses are all on showing positive trends, he said. "If you look at how we've turned this thing around, I feel we're going to continue to see momentum in 2013, so we're expecting a good year."